Question

Suppose that in the absence of any corrective measures, the economy generates 750 megatonnes (Mt) of GHG emissions (E) per year. The damage created by an additional Mt of emissions is called the marginal damage. Assume the marginal damage function is MD=0.04 E. Thus, if E= 750 Mt, the additional damage to society associated with one more Mt of emissions is $30. The marginal abatement cost, the additional cost associated with a one Mt reduction in emissions, is given as MAC = 45 - 0.06 E. When there is no abatement, E = 750 Mt and the marginal cost of abatement is zero. a. Draw the figure described above with emissions measured on the horizontal axis in megatonnes per year and dollars on the vertical axis. b. If E = 600 Mt, how much abatement (emissions reduction) has occurred? What is the marginal cost associated with lowering emissions by an additional Mt when E = 600? What is the marginal benefit of an additional Mt reduction in emissions when E = 600 (i.e., what is the marginal damage prevented)? c. If E = 600, calculate total abatement costs. Calculate total benefits from lower emissions. d. For this economy, what is the socially optimal level of emissions, E*? e. Suppose the government imposed a tax on emissions equal to $12 per Mt of greenhouse gas emissions. How does the tax affect total emissions in the economy? Is the tax sufficient to reduce emissions to E*? Why or why not?

Answer 1

dollay D o 100 200 300 400 500 600 700 MAC MAC b) Given that E = 600 marginal abatemnt cost MAC = 45-0.06E morginal damage-0-04x600 - 45-10.06X600) = 9, -24 The additional emmission at E=600 causes damage of qand 24 c) Triangular area under MAC blm 600 and 750 can be calculated using formula of area of triangle - half y base x height = $x 150x8 = $450 Now to calculate area under MD extend the line at 600 Upto MO CUTVE draw horizontal line from that point which touches line at yo to MD. you will be able to see one rectangle between Goo and 450 and one triangle = are a of rectangle + area of triangle = (150-600) x 240 + 0.51750-600)*(30-24) = 3600 + 450 = $ 4050 dy the optimal point is where the MD meets MAC 0.04€ = 45 -0-06 € 0.04€ + 0.06€ = 45 0-1E = 45 E-450 optimal level of emission is 450 tax the level of emiss e with imposition of emission becomes most costly for the firm.